Given $x,y,z\in \mathbb{R^+}$. Find all sets of $x,y,z$ that correspond to $$x+y+z=x^2+y^2+z^2+18xyz=1$$(Zhuge Liang)
Problem
Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) p5 sl-6 https://artofproblemsolving.com/community/c3196914_mathcenter_contest
Tags: algebra, system of equations, System